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on Game Theory |
| By: | Xu, Jin; Zenou, Yves; Zhou, Junjie |
| Abstract: | We study a very general contest game in which players exert efforts in multiple battles. The conflict structure, which represents who participates in which battlefield, is arbitrary and can be represented by a hypergraph. We show, under mild conditions on the cost function and contest technology, that the set of pure strategy Nash equilibria is nonempty and convex, and provide equivalent characterizations using techniques from Variational Inequality (VI). We demonstrate that the strong monotonicity of the cost function always implies the uniqueness of Nash equilibrium regardless of the conflict structure. We also perform an extensive comparative statics analysis with respect to the parameters of the model and discuss several applications of our model. Our general model incorporates many existing models of single or multi-battle contests as special cases when the conflict network and/or the cost function take particular forms. |
| Keywords: | Contests; network games; variational inequality |
| JEL: | C72 D74 D85 |
| Date: | 2019–04 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:13647&r=all |
| By: | Blume, Larry (Cornell University and Institute for Advanced Studies); Meier, Martin (University of Bath and Institute for Advanced Studies) |
| Abstract: | In strategic-form games Selten's (1975) perfect equilibria are admissible. This is not true for extensive-form perfection. Quasi-perfect equilibria solves this problem using Selten's (1975) trembles to introduce a refinement of Nash equilibrium wherein each player puts infinitesimal weight on other players's strategies, but not her own. One might be sure of oneself, while (infinitesimally) unsure of others. However, also quasi-perfection itself is not without problems, precisely because it ignores future infinitesimal uncertainties in one's own play. We introduce a refinement; perfect quasi-perfect equilibrium, to capture the best of both concepts. Our idea is to force each player to consider infinitesimal deviations in her own future play, but to make them so unlikely that they are infinitely less likely than the combined likelihood of deviations by all other players. Our refinement uses only strategies that are neither weakly dominated in the strategic form nor in the agent normal form. |
| Date: | 2019–03 |
| URL: | http://d.repec.org/n?u=RePEc:ihs:ihswps:4&r=all |
| By: | Gabriele Camera (Economic Science Institute, Chapman University & University of Bologna); Cary Deck (University of Alabama & Chapman University); David Porter (Economic Science Institute, Chapman University) |
| Abstract: | We explore if fairness and inequality motivations affect cooperation in indefinitely repeated games. Each round, we randomly divided experimental participants into donor-recipient pairs. Donors could make a gift to recipients, and ex-ante earnings are highest when all donors give. Roles were randomly reassigned every period, which induced inequality in ex-post earnings. Theoretically, income-maximizing players do not have to condition on this inequality because it is payoff-irrelevant. Empirically, payoff-irrelevant inequality affected participants’ ability to coordinate on efficient play: donors conditioned gifts on their own past roles and, with inequalities made visible, discriminated against those who were better off. |
| Keywords: | cooperation, experiments, indefinitely repeated games, social dilemmas |
| JEL: | C70 C90 D03 E02 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:chu:wpaper:19-09&r=all |
| By: | Giuseppe Attanasi (Université Côte d'Azur, CNRS, GREDEG, France); Kene Boun My (BETA, Université de Strasbourg); Nikolaos Georgantzís (Burgundy School of Business & Economics Department, Universitat Jaume I); Miguel Ginés (Economics Department, Universitat Jaume I) |
| Abstract: | In a two-stage investment-effort game, we model altruistic investment in another agent's capacity to benefit from synergies between the two agents' efforts. Contrary to most models in the literature on altruism, we assume that agents who invest in others have no direct utility from their giving behavior, ruling out any genuinely altruistic component in their utility function, i.e., stemming from other-regarding preferences. Furthermore, we disentangle this strategic ethics" from reputational e ects yielding incentives for a more pro-social action in the present in order to favor Pareto-superior outcomes in the future. Isolated consumption of one's own bene ts from own efforts is the worst equilibrium, which is globally stable and is shown to exist independently of the investment cost. However, for a low enough investment cost, there exist two alternative equilibria: an unstable intermediate equilibrium in which both agents make positive complementarity-building investments, and a stable one in which both agents invest all they can to complementarity building. Both equilibria Pareto-dominate the aforementioned no-investment equilibrium. Results of a laboratory experiment con rm our behavioral prediction that, for a low enough investment cost, subjects coordinate on positive complementarity-building investment, which in turn boosts their effort in the second stage. The latter increases in both own and others' complementarity-building investment, as predicted by our model. All this holds independently of subjects' risk and inequity aversion. The latter suggests that complementarity-building investment is not motivated by altruism. Rather, it is purely strategic. |
| Keywords: | Complementarity-building Investment, Strategic Complementarities, Altruism, Fairness, Risk Aversion |
| JEL: | C72 C73 C91 D64 |
| Date: | 2019–04 |
| URL: | http://d.repec.org/n?u=RePEc:gre:wpaper:2019-13&r=all |
| By: | FOERSTER Manuel, (Universität Hamburg); MAULEON Ana, (Université Saint-Louis Bruxelles and CORE, UCLouvain); VANNETELBOSCH Vincent, (CORE, UCLouvain) |
| Abstract: | We propose a framework of network formation where players can form two types of links: public links are observed by everyone and shadow links are only observed by neighbors. We introduce a novel solution concept called rationalizable peer-confirming pairwise stability, which generalizes Jackson and Wolinsky (1996)’s pairwise stability notion to accommodate shadow links. We then study the case when public links and shadowlinks are perfect substitutes and relate our concept to pairwise stability. Finally, we consider two specific models and show how false beliefs about others’ behavior may lead to segregation in friendship networks with homophily, reducing social welfare. |
| Keywords: | network formation, peer-confirming beliefs, private information, rationalizability, shadow links, stability |
| JEL: | A14 C70 D82 D85 |
| Date: | 2018–10–01 |
| URL: | http://d.repec.org/n?u=RePEc:cor:louvco:2018030&r=all |
| By: | Mira Frick (Cowles Foundation, Yale University); Ryota Iijima (Cowles Foundation, Yale University); Yuhta Ishii (Harvard University) |
| Abstract: | We take an equilibrium-based approach to study the interplay between behavior and misperceptions in coordination games with assortative interactions. Our focus is assortativity neglect, where agents fail to take into account the extent of assortativity in society. We show, ?rst, that assortativity neglect ampli?es action dispersion, both in ?xed societies and by exacerbating the e?ect of social changes. Second, unlike other misperceptions, assortativity neglect is a misperception that agents can rationalize in any true environment. Finally, assortativity neglect provides a lens through which to understand how empirically documented misperceptions about distributions of population characteristics (e.g., income inequality) vary across societies. |
| Keywords: | Assortativity neglect, Coordination games, Self-confirming equilibrium, Misperception |
| JEL: | C70 D80 D85 |
| Date: | 2018–04 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:2128r&r=all |
| By: | Chiara Donnini (Università di Napoli Parthenope); Maria Laura Pesce (Università di Napoli Federico II) |
| Abstract: | We investigate the fairness property of equal-division competitive market equilibria (CME) in asymmetric information economies with a space of agents that may contain non-negligible (large) traders. We first propose an extension to our framework of the notion of strict fairness due to Zhou (1992). We prove that once agents are asymmetrically informed, any equal-division CME allocation is strictly fair, but a strictly fair allocation might not be supported by an equilibrium price. Then, we investigate the role of large traders and we provide two sufficient conditions under which, in the case of complete information economies, a redistribution of resources is strictly fair if and only if it results from a competitive mechanism. |
| Keywords: | Asymmetric information, mixed markets, strict fairness, competitive equilibrium. |
| JEL: | D43 D60 D82 |
| Date: | 2019–04–08 |
| URL: | http://d.repec.org/n?u=RePEc:sef:csefwp:528&r=all |
| By: | Fabien Gensbittel (TSE - Toulouse School of Economics - Toulouse School of Economics); Marcin Peski (University of Toronto); Jérôme Renault (TSE - Toulouse School of Economics - Toulouse School of Economics) |
| Abstract: | We revisit the question of modeling incomplete information among 2 Bayesian players, following an ex-ante approach based on values of zero-sum games. K being the finite set of possible parameters, an information structure is defined as a probability distribution u with finite support over K × N × N with the interpretation that: u is publicly known by the players, (k, c, d) is selected according to u, then c (resp. d) is announced to player 1 (resp. player 2). Given a payoff structure g, composed of matrix games indexed by the state, the value of the incomplete information game defined by u and g is denoted val(u, g). We evaluate the pseudo-distance d(u, v) between 2 information structures u and v by the supremum of |val(u, g) − val(v, g)| for all g with payoffs in [−1, 1], and study the metric space Z * of equivalent information structures. We first provide a tractable characterization of d(u, v), as the minimal distance between 2 polytopes, and recover the characterization of Peski (2008) for u v, generalizing to 2 players Blackwell's comparison of experiments via garblings. We then show that Z * , endowed with a weak distance d W , is homeomorphic to the set of consistent probabilities with finite support over the universal belief space of Mertens and Zamir. Finally we show the existence of a sequence of information structures, where players acquire more and more information, and of ε > 0 such that any two elements of the sequence have distance at least ε : having more and more information may lead nowhere. As a consequence, the completion of (Z * , d) is not compact, hence not homeomorphic to the set of consistent probabilities over the states of the worldàworldà la Mertens and Zamir. This example answers by the negative the second (and last unsolved) of the three problems posed by J.F. Mertens in his paper "Repeated Games", ICM 1986. |
| Date: | 2019–03–22 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-02075905&r=all |
| By: | Encarnación Algaba (Matemática Aplicada II and Instituto de Matemáticas de la Universidad de Sevilla, Escuela Superior de Ingenieros, Sevilla, Spain); Sylvain Béal (Université de Bourgogne Franche-Comté, CRESE); Eric Rémila (Université de Saint-Etienne, Gate); Phillippe Solal (Université de Saint-Etienne, Gate) |
| Abstract: | This paper deals with Harsanyi power solutions for cooperative games in which partial cooperation is based on specific union stable systems given by the winning coalitions derived from a voting game. This framework allows for analyzing new and real situations in which there exists a feedback between the economic influence of each coalition of agents and its political power. We provide an axiomatic characterization of the Harsanyi power solutions on the subclass of union stable systems arisen from the winning coalitions from a voting game when the influence is determined by a power index. In particular, we establish comparable axiomatizations, in this context, when considering the Shapley-Shubik power index, the Banzhaf index and the Equal division power index which reduces to the Myerson value on union stable systems. Finally, a new characterization for the Harsanyi power solutions on the whole class of union stable systems is provided and, as a consequence, a characterization of the Myerson value is obtained when the equal power measure is considered. |
| Date: | 2018–11 |
| URL: | http://d.repec.org/n?u=RePEc:crb:wpaper:2018-05&r=all |
| By: | Sylvain Béal (Université de Bourgogne Franche-Comté, CRESE); Issofa Moyouwou (Department of Mathematics, University of Yaounde I - Cameroon); Eric Rémila (Université de Saint-Etienne, Gate); Phillippe Solal (Université de Saint-Etienne, Gate) |
| Abstract: | A situation in which a finite set of agents can obtain certain payoffs by cooperation can be described by a cooperative game with transferable utility, or simply a TU-game. In the literature, various models of games with restricted cooperation can be found, in which only certain subsets of the agent set are allowed to form. In this article, we consider such sets of feasible coalitions that are closed under intersection, i.e., for any two feasible coalitions, their intersection is also feasible. Such set systems, called intersection closed systems, are a generalization of the convex geometries. We use the concept of closure operator for intersection closed systems and we define the restricted TU-game taking into account the limited possibilities of cooperation determined by the intersection closed system. Next, we study the properties of this restricted TU-game. Finally, we introduce and axiomatically characterize a family of allocation rules for games TU-games on intersection closed systems, which contains a natural extension of the Shapley value. |
| Date: | 2018–12 |
| URL: | http://d.repec.org/n?u=RePEc:crb:wpaper:2018-06&r=all |
| By: | Luís Sá (University of Minho, Department of Economics/NIPE); Luigi Siciliani (University of York, Department of Economics and Related Studies); Odd Rune Straume (University of Minho, Department of Economics/NIPE) |
| Abstract: | We develop a dynamic model of hospital competition where (i) waiting times increase if demand exceeds supply; (ii) patients differ in their evaluation of health benefits and choose a hospital based on waiting times; and (iii) there are penalties for providers with long waits. We show that, if penalties are linear in waiting times, a more competitive dynamic environment does not affect waiting times. If penalties are instead non-linear, we find that waiting times are longer under the more competitive environment. The latter result is derived by calibrating the model with waiting times and elasticities observed in the English NHS for a common treatment (cataract surgery), which also shows that the difference between waiting times under the two solution concepts is quantitatively small. Policies that facilitate patient choice, an alternative measure of competition, also lead to higher steady-state waiting times, and tougher penalties exacerbate the negative effect of choice policies. |
| Keywords: | Hospital competition; waiting times; differential games. |
| JEL: | C73 H42 I11 I18 L42 |
| Date: | 2018 |
| URL: | http://d.repec.org/n?u=RePEc:nip:nipewp:20/2018&r=all |
| By: | Giovanna D'Adda; Martin Dufwenberg; Francesco Passarelli; Guido Tabellini |
| Abstract: | We consider an expanded notion of social norms that renders them belief-dependent and partial, formulate a series of related testable predictions, and design an experiment based on a variant of the dictator game that tests for empirical relevance. Main results: Normative beliefs influence generosity, as predicted. Degree of partiality leads to more dispersion in giving behavior, as predicted. |
| Keywords: | social norms, partial norms, normative expectations, consensus, experiment |
| JEL: | C91 D91 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_7568&r=all |
| By: | Bergantiños, Gustavo; Navarro, Adriana |
| Abstract: | In this paper we provide an axiomatic characterization of the painting rule for minimum cost spanning tree problems with multiple sources. The properties we need are: cone-wise additivity, cost monotonicity, symmetry, isolated agents, and equal treatment of source costs. |
| Keywords: | minimum cost spanning tree problems with multiple sources, painting rule, axiomatic characterization. |
| JEL: | C71 |
| Date: | 2019–04–12 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:93266&r=all |
| By: | Kalus Abbink; Donna Harris |
| Abstract: | We study in-group favouritism and out-group discrimination in a novel multiplayer dictator game in a naturally occuring setting. An allocator divides a large sum of money among three groups of around 20 recipients each and to Self. The groups are supporters of two rival political movements in Thailand and politically neutral subjects. The non-rival out-group as a reference point allows us to measure in-group favouritism and out-group discrimination. A treatment with artificial groups serves as a control. We find both in-group favouritism and out-group discrimination among the naturally occurring groups. In artificial groups, favouritism is observed, but not discrimination. Our results suggest that the two behaviours are not driven by the same motive, and only when groups are in conflict out-group discrimination is likely to occur. |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:csa:wpaper:2019-02&r=all |
| By: | Nataliya Gerasimova (Norwegian School of Economics (NHH) - Department of Finance); Eric Jondeau (UUniversity of Lausanne - Faculty of Business and Economics (HEC Lausanne); Swiss Finance Institute) |
| Abstract: | We develop a framework for the strategic interaction between a hedge fund and a prime broker. The hedge fund optimally determines its cash holdings and the fraction of shorted securities. The prime broker optimally determines its cash holdings, the margin rates, and the rehypothecation rate. The hedge fund and the prime broker make optimal decisions to maximize their expected return on equity. We describe how the evolution of market returns affects the equity of the hedge fund and may force it to delever or even default. Because an eventual default of the hedge fund would severely affect the prime broker’s performance, the prime broker determines the lending rate to cover its expected loss in case of a default. We then explore the strategic interaction between hedge fund and prime broker decisions by calibrating and solving our model for realistic parametrizations. We find that this interaction may give rise to some undesirable implications, such as an increase in overall risk and leverage, when the regulator controls only the prime broker’s balance sheet. |
| Keywords: | Hedge fund, Prime broker, Leverage, Balance sheet, Financing decisions |
| JEL: | G2 G23 G24 |
| Date: | 2018–08 |
| URL: | http://d.repec.org/n?u=RePEc:chf:rpseri:rp1854&r=all |
| By: | Kanehara, Daishoku; Kamei, Keita |
| Abstract: | This study incorporates transport price and endogenous product differentiation in an international oligopoly. Assuming endogenous determination of transport price based on the profit maximization of the transporter and using a three-stage game, we analyze the effect of the degree and difficulty of product differentiation on transport price. We show that both negatively affect the endogenous transport price. The intuition of this result comes from that the positive effect of a decrease in endogenous transport price on the demand for the differentiated products is greater than the negative effect on the price. |
| Keywords: | Endogenous Product Differentiation; International Trade; Oligopoly; Product R&D; Transport Price. |
| JEL: | F12 L13 L16 O1 |
| Date: | 2019–04–07 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:93148&r=all |
| By: | Roberto Galbiati (Département d'économie); Emeric Henry (Département d'économie); Nicolas Jacquemet (Centre d'économie de la Sorbonne (CNRS/UP 1)) |
| Abstract: | How does the exposure to past institutions affect current cooperation? While a growing literature focuses on behavioral channels, we show how cooperation-enforcing institutions affect rational learning about the group’s value. Strong institutions, by inducing members to cooperate, may hinder learning about intrinsic values in the group. We show, using a lab experiment with independent interactions and random rematching, that participants behave in accordance with a learning model, and in particular react differently to actions of past partners whether they were played in an environment with coercive enforcement or not. |
| Keywords: | Enforcement; Social values; Cooperation; Learning spillovers; Persistence of institutions; Repeated games; Experiments |
| JEL: | C91 C73 D02 K49 P16 Z1 |
| Date: | 2019–04 |
| URL: | http://d.repec.org/n?u=RePEc:spo:wpmain:info:hdl:2441/6unm655ita9ojbuuc83c9h0is8&r=all |
| By: | Breitmoser, Yves (Bielefeld University); Schweighofer-Kodritsch, Sebastian (HU Berlin and WZB Berlin) |
| Abstract: | Li (2017) supports his theoretical notion of obviousness of a dominant strategy with experimental evidence that bidding is closer to dominance in the dynamic ascending-clock than the static second-price auction (private values). We replicate his experimental study and add three intermediate auction formats to decompose this behavioral improvement into cumulative effects of (1) seeing an ascending-price clock (after bid submission), (2) bidding dynamically on the clock and (3) getting drop-out information. Li\'s theory predicts dominance to become obvious through (2) dynamic bidding. We find no significant behavioral effect of (2). However, both (1) and (3) are highly significant. |
| Keywords: | ; |
| Date: | 2019–04–08 |
| URL: | http://d.repec.org/n?u=RePEc:rco:dpaper:151&r=all |
| By: | Frédéric Gavrel (CREM - Centre de recherche en économie et management - UNICAEN - Université de Caen Normandie - NU - Normandie Université - UR1 - Université de Rennes 1 - UNIV-RENNES - Université de Rennes - CNRS - Centre National de la Recherche Scientifique) |
| Abstract: | In a status game, homogenous individuals first decide on their income (and on the effort necessary to that end) with the aim of Getting ahead of the Smiths (GAS). Next, they make use of a pure positional good to make incomes visible. Although the GAS hypothesis is ordinal, the signaling costs induce cardinal social concerns. The GAS hypothesis, translated into the pure pride concern, generates an equilibrium in which identical agents have unequal income levels. Because individuals decide on their income without taking into account its effect on the signaling costs of higher-ranked participants, this equilibrium is inefficient. Introducing a Pigovian tax to reduce conspicuous consumption generates a rat-race effect in the income-setting stage which neutralizes the effect of this tax on utilities. But a redistributive income tax, if coupled with an appropriate Pigovian tax on conspicuous consumption, increases all utilities. |
| Keywords: | Status game,Social concerns,Income inequalities,Conspicuous con- sumption,Income redistribution,Well-being,Efficiency |
| Date: | 2019–03–29 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:halshs-02083460&r=all |
| By: | Thomas Eichner; Rüdiger Pethig |
| Abstract: | In a two-country economy we analyze how tax competition differs from the standard all-Nashian tax competition, if one or both countries are Kantians in Roemer’s sense. Kantians are shown to choose a higher tax rate than Nashians for any given tax rate of the other country, which indicates that they seek to mitigate the (Nashian) race to the bottom. We avoid dealing with multiple equilibria by assuming that capital is sufficiently scarce, and we find for symmetric countries that the all-Kantian tax competition is efficient and that the inefficient race to the bottom is weakened in economies with a Nashian and a Kantian. That confirms the intuitive idea that countries following the Kantian categorical imperative avoid or at least soften the socially undesirable impact of (Nashian) self-interest. We also investigate the incentives of opportunistic countries to choose Nashian or Kantian behavior out of self-interest and find that either both governments choose to behave as Kantians or that - under different conditions - the robust Nashian selfinterest supersedes Kantian moral principles such that the inefficient all-Nashian tax competition results. |
| Keywords: | tax competition, best reply, Kantian, Nashian, endogenous behavior selection |
| JEL: | H73 H87 C72 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_7571&r=all |